Rim thickness. The 30-06 is thicker. I have 1903s. Strippers i use in my 1917 eddiestone but could only find about 15 or 20. But i found a bunch of 308s so i bought some. Wouldnt work. Its to thick. Now you may try to bend it a little. It should work then somewhat.

I use mine for 308 and 30.06 and have done so since 1973. Now if you have brass that was fired in M1 Garand the rims may be burred and cause a problem but even 8MM Mauser stripper clips work just fine.